Preheat the oven to 400°F.
Toss the cabbage together with the leeks in a 12-inch cast-iron skillet. Drizzle with 2 tbsp olive oil and sprinkle with 1 tsp of the salt. Toss to combine.
In a small bowl, stir together the whole grain mustard, remaining olive oil, apple cider vinegar, brown sugar and garlic. Sprinkle the chicken all over with the remaining salt and pepper. Rub the mustard mixture all over the chicken. Set chicken over the cabbage.
Roast the chicken until its internal temperature reaches 165.
Make the mustard sauce. In a medium skillet over medium heat, add the olive oil. Once the oil is glistening, add the shallot and cook until translucent, 5 min. Stir in the white wine and cook, stirring, until reduced by half, about 3 min. Stir the whole grain mustard and Dijon mustard until smooth, slowly add in the chicken stock and the heavy cream.
Stir in the tarragon. Simmer until thickened enough to coat the back of the spoon.